e side of each of the discs is written a number and on the other the
name of the note. They are fitted by the child into the corresponding
places.]

[Illustration: FIG. 34.

The child next arranged the discs in the notes cut out on
the staff, but there are no longer numbers written to help him find the
places. Instead, he must try to remember the place of the note on the
staff. If he is not sure he consults the numbered board (Fig. 33).]

[Illustration: FIG. 35.

The child arranged on the staff the semitones in the
spaces which remain where the discs are far apart: do-re, re-mi, fah-soh,
soh-la, la-ti. The discs for the semitones have the sharp on one side and
the flat on the other, e.g., re[sharp]-mi[flat] are written on the
opposite sides of the same disc.]

[Illustration: FIG. 36.

The children take a large number of discs and arrange them
on the staff, leaving uppermost the side which is blank, i.e., the side
on which the name of the note is not written. Then they verify their work
by turning the discs over and reading the name.]

[Illustration: FIG. 37.

The double staff is formed by putting the two staves
together. The children arrange the notes in the form of a rhombus.]

[Illustration: FIG. 38.

The two boards are then separated and the notes remain
arranged according to the treble and bass clefs. The corresponding key
signatures are then placed upon the two different staves.]

ARITHMETIC

The children possess all the instinctive knowledge necessary as a
preparation for clear ideas on numeration. The idea of quantity was
inherent in all the material for the education of the senses: longer,
shorter, darker, lighter. The conception of identity and of difference
formed part of the actual technique of the education of the senses,
which began with the recognition of identical objects, and continued
with the arrangement in gradation of similar objects. I will make a
special illustration of the first exercise with the solid insets,
which can be done even by a child of two and a half. When he makes a
mistake by putting a cylinder in a hole too large for it, and so
leaves _one_ cylinder without a place, he instinctively absorbs the
idea of the absence of _one_ from a continuous series. The child's
mind is not prepared for number "by certain preliminary ideas," given
in haste by the teacher, but has been prepared for it by a process of
formation, by a slow building up of itself.

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